Algebraic Comparison (aka Inequalities, Quantitative Comparison etc)

You know those questions that come up all the time? Inequalities with algebra, quantity comparison, cubing, squaring, fractions, guessing numbers, all that jazz? This video will try to demystify much of algebraic comparison. Do leave a like if you learn something or enjoyed solving the examples, crafted by hand by me!

The GRE and GMAT are two of most used graduate exams for those seeking to study a Masters Degree or Masters in Business Administration (MBA) degree. The Graduate Record Exam and Graduate Management Admissions Test have been taken for over 50 years and are taken by approximately 600,000 and 300,000 people worldwide annually, respectively. These exams are typically taken between the ages of 18-40, by those who have completed, or are about to complete, their Bachelors Degree.

[shreshthsaha]

The key takeaway was the 3 golden rules:

1. Substitute with positive and negative integers.
2. Substitute with positive and negative fractions.
3. Take care of the equality/inequality symbols.

Thank you for making Math visually appealing.

[akashmishra]

So glad I watched your picking numbers video before this, and the [ -2, -1/2, 1/2, 2] set works mostly all of the time. Thanks Phillip <3

[kwamebflat]

Excellent videos, Philip. I'm learning a lot! For the first example, I moved the b2 to the left hand side and equated it to 0. Then I realised the equation is a difference of 2 squares (a-b)(a+b) meaning that a=b or a=-b, making me choose answer choice D.

[Leonardich]

Hi, for the last question, it is just C < -1, not that C < -1 and is an integer. Try C = -3/2, otherwise, everything else is the same. A more general approach is to split into four groups as such: --(-1)--(0)--(1)--, so you have four intervals to check because in your case you are not taking into account pos/neg fraction greater/less than +1/-1.

[bukolaessien]

Woohoo.. I got the last one!! I've been so so scared of comparisons for long. Thanks so much again Philip

[IbiyeTam-George]

I got the last question! I’m so happy. Thank you Philip

[MrMcfire]

A very useful technique indeed - GRE really are always looking to trick you! The way I think about it is if the question looks too easy, then there is almost always a trap somewhere...

[prabeshkhanal]

Thank you so much Philip. You've been of great help. Love from Nepal.

[sigurdlongva]

Great video, as always. Just a small correction regarding the last question: c does not necessarily have to be a negative integer. It can be any negative NUMBER smaller than -1 (like negative 3/2). It does not make any difference for the solution to the question, but it can be important to bear this difference in mind for other questions.

[iyanuoluwaaliu]

🕺🕺🕺 I got everything right. Thanks a lot, Philip for making me a better student 😊👏🏿👏🏿

[snehashisnag]

If we consider a=1 in the third question, then also the inequality doesn't hold ground. So we can't say that all positive integers work.

[prajaktachavan]

You are just brilliant! why did'nt I see your videos earlier😪

[Nazish]

Since c will be a negative integer and every -ve integer satisfies, except -1 where -1<1<(-1)^2 == -1<1<1 which essentially negates our initial assumption of c being -ve integer. Hence D can be our only choice. This is for last question.

[yashwaingankar]

I wish our Engineering professor taught like the way you do...my GPA would have been above 3.5 🙂

[lubainabhori]

Your videos are favourite part of my preparation..

[puneet.fitness]

Dear Philip can you please go through the below question

If g(x)=3x+√x​, find g(d2+6d+9).

[bradleygoronson]

I got the last question right! Thanks for all your videos Phillip! This framework for thinking through these questions is great.

[hansiwelangoda]

Thank you very much Philip for your excellent teaching style.youre the best🙏

[mskvlogs]

Great work Philip!! You will never disappoint with all your analysis. Thanks for being our Virtual Professor 🤗

[amithasan]

Excellent Video to Crack Hard QC Questions! Thanks!